Visual aid for mathematics



May 9, 195 J. F. scHAcHT 2,507,460

VISUAL AID FOR MATHEMATICS i; Filed Oct. 3, 1946 3 Sheets-Sheet l JNVENToR.

May 9, 1950 J. F. scHAcHT VISUAL AID FOR MATHEMATICS 3 Sheets-Sheet 2 `Filed Oct. 3, 1946 INVENTOR. fo/77; j "qcizac/ZZ,

BY I May 9, 1950 J. F. scHAcH-r VISUAL AID FOR MTHEMATQCS 3 Sheets-Sheet 3 Filed Oct. 5, 1946 dbh@ INJfBlI v//I/IIIAJlI/rllrl 111111111111111 Patented May 9, 1950 UNITED STATES PATENT OFFICE VISUAL AID FOR MATHEMATICS* Application October 3, 1946, SerialNo.v 701,006

(CRBS-34') 4 Claims.

This invention relates to new and improved devices for' use as visual aids in instruction in mathematics and more specifically to devices in the form of triangles, quadrilaterals or other gures in whichV the lengths of the sides and their angular relationship may be varied.

The construction may be used in the form of two or three dimensional figures and may include lines intersecting sides or angles at desired anglesv in addition to the sidesv or lines defining the figures. Devices of this character are of material aid in teaching classes in related subjects such as 'geometry and trigonometry and assist the student in visualizing the iigure and its various' properties. The iigures are continuously variable as to length of side and angular relationships so that the student may visualize the various. forms the figure may take.

It is' an objectl of the present invention to provide new and improved visual aids for use in connection with mathematical instruction or study.

It is--a further object to provide devices which are readily adjustable as to dimensions and angular relationship.

'It is an additiona1 object to provide devices in which flexible members are `provided to dene and show interior relationships as to areas and angles within a gure defined by the device.

It vis also an object to provide devices which are simple in design and construction and adapted forv commercial production and use.

Other and further objects will appear as the description proceeds.

I have shown certain preferred embodiments oi my invention in the accompanying drawings, in which.-

'Figure- 1 is a plan View of one form of construction-showing a triangle;

VFigure 2 is a partly broken away elevation of one side of the triangle;

Figure 3 is an enlarged section taken on line 3'-30'f Figure 2;

Figure 4 is a plan View similar to Figure 1 but showing a modiiied form of construction;

Figure 5- is a lpartly broken away elevation, on an enlarged scale, of one side of Figure 4;

Figure 6 is a plan view of a construction similar to Figure 4 but applied to a four sided gure; and

"Figure 7 is an eleva-tion, partlyl broken away,v showing one side of Figure 6- on anenlarged scale.Y

Referring first to the form of construction shown in Figure l, this showsL a triangular figure having the three similar side assemblies H, I2 and I3 pivoted at their ends by pivot membersL I4, I5 and I5. Each side assembly comprises a pair of interfitted members |1 and I8 soA designed' so that they may be slid relative to each other to cause the side assembly to have differing lengths, as desired, between its end pivots. The members Il and I8 are provided with the elongated slotsv 2| andl 2,2, respectively, which receive guide pins carried bythe adjacent member.

As shown in Figure 2, the upper member carries thev pivot ypin ItA at its left end for connection to the adjacent side assembly |2. At itsy righ-t end, as shown in the lowerv portion -of Figure 2, this ymem-ber I1 carries the pin 23 lwhich slides in the slot 22 in member I8. A block 24y is provided fitted on pin 23 and located between members |1S and lI 8 in order to maintain the proper spacing. As shown in Figure 2, the upturned edge 2B of member |81 is provided with a plurality of. evenly spacedv circular openings 21. In Figure 3, the downturned edge 28 of member I1 is show-n as provided with a similar series of openings 29. The star wheel or gear wheel 30 is tted between the `mem-bers |11 and I8 on the pivot member 3|, the points of the star wheel fitting into the opposite series of openings 21 and 29.

As best shown in Figure 1, the pivot members I4, I5 and I5 are provided with connecting `lugs 3.4, 35 and 36. The pivot pin 3| carries a plurality of lugs 3.1., 38 and 39 similar to the lugs carried by the corner pivot members. These various connecting lugs are connected, as shown in Figure 1, to other lugs by means of extensible members 4U. The-se members 40' are preferably formedl ofv material such as rubber which Yis capable of considerable extension while remaining in a straight liney between `the two points to which it is connected.

In the assembly of the parts, the star wheels 30 are located relative to members |'1 and I8 lso that they are spaced halfway between the end pivots vI5 and I6. As will be apparent from Figure-l, the threesides IUI, |'2 and I3 are all identical and are provided `with multiple members 40 between the several connectingV lugs. It' will be apparent that when the connections |1 and I8 of any side 'assembly are slid relative. to eachother inA either-directionrwthin the limits oftmovement,V

3 the star wheel will maintain the pivot pin 3| at a point halfway between the adjacent end pivots I4, l5 and I6.

The form of construction shown in Figures 4 and 5 differs from that shown in Figures l, 2 and 3 in that the sides themselves are not extensible. As shown in Figure 4, the triangle is provided with the three side members 5|, 52 and 53. The member 52 is shown in elevation and partly broken away in Figure 5. This member 52 has a downturned edge 54 to stiften the member. It is provided with a longitudinal slot 55 into which is fitted a pin 56 which may be slid lengthwise of the slot to any desired position. This pin 56 carries a protractor in the form of a graduated semi-circle 51. The protractor is maintained in proper relationship to the member 52 by means of a U-shaped member 58 held to the protractor by rivets '59 and having downturned ends 60 which slide in the slot 55.

The pin 56 also carries three connecting lugs 6l, 62 and 63 which are connected by exible extension members 61S to similar lugs on adjacent side elements and to lugs 65, 66 and 6l carried on the corner pivot pins 68, 69 and 10. These corner pins are iixedly secured in one side member and slide in the elongated slot in the adjacent corner member.

. The several side members 5l, 52 and 53 are all identical in construction and it will be apparent I;

that each may have a greater or less portion of its length included in the triangle formed by the three members within the limits oi the movement of the elongated slot formed in the member. The center pins are not mounted in the center oi the side as in the construction of Figures l to 3, but may be slid to any desired point within the limits of the slot. In order that the relative location of the center sliding pins and the protractor may be determined, each member 5l, 52 and 53 is provided with a scale, the zero point of which is the xed pivot member carried by that side. It will be noted that the corner pivot members 58, E9 and 'i0 are provided also with protractors l2, 13 and 14. Thus, by means ci the various protractors, the angles between the sides of the triangle may be read on and also the angles formed by the connections Gd with the points located along the sides or at the corners of the iigure may be read.

The form of construction shown in Figures 6 and '7 is similar to that shown in Figures 4 and 5 with the exception that four sides 8l, 32, 83 and 84 are provided. Thus, the device may be used to determine the relationships between the angles in different forms of four sided iigures. They also show visually the relationships between lines connecting midpoints oi the sides with the other midpoints or with the angles formed by the junctions o the sides of the iigure. In this case, also, the sides are provided with scales as the protractor slidably carried by each side is not limited to the midpoint, but may be placed on any point desired on the side.

While I have shown only triangular and four sided gures in examples given in the drawings, it will be understood that the invention is not limited as to the number of sides which may be provided, nor is it limited to plane figures. The construction is useful in the teaching of the relationships of the parts of triangles, quadrilaterals or other figures to other parties and may be adjusted, as desired, Vduring the instruction of an individual or large classes. It is also useful in 4 connection with individual study of the properties of such iigures.

While I have shown certain preferred embodiments of my invention, these are to be understood to be illustrative only as it is capable of variation to meet dierent conditions and requirements, and I contemplate such modifications as come within the spirit and scope of the appended claims.

I claim:

l. A mathematical device comprising at least three side units pivotally connected together at iixed points adjacent their ends to form a gure deiined by the units, each unit comprising members slidable relative to each other for varying the lengths of the units, devices carried by the units engaging the members and thereby maintained at the mid points of said units throughout their variation in length, and further members connecting the mid point devices of certain of the units, said further members being extensible to conform to diierent adjustments of the units.

2. A mathematical device comprising at least three side units pivotally connected together at fixed points adjacent then' ends, said units each comprising a pair of slidably connected elements, 11i-reconnecting pivots being on the diiierent elements oi the pair whereby the eiective figure forming length of said units is adjusted by sliding the elements relative to each other, rotating members associated with each pair of elements at the mid point of the pair and coacting with each element or" the pair to maintain them at the mid point upon sliding of the elements relative to one another, and extensible members connected to the mid points rotating members of certain of the units and connected to other portions of the figure formed by the units, the connection of said extensible members to the mid points of the units being maintained during adjustment of the length of said units.

3. A methernatical device comprising at least three side units pivotally connected together, the pivots being xed relatively to at least one end of each unit, each unit comprising a pair of elements slidable relative to each other for adjusting the effective figure forming length of each unit, rotatable members between each pair of elements, said rotatable members having a geared connection with each element, said rotatable members forming intermediate .points in xed relation between the two ends, a plurality of members extending from said intermediate points of each of the units and connected to intermediate points and pivot points of other side units of the figure formed by the units, the points of connection of said members to the units being maintained by the geared connection in predetermined relationship to the pivot ends of the units during adjustment of the effective lengths of the units, said last members being extensible to conform to diii'erent adjustments of the units.

a. A mathematical device comprising three side units pivotally connected together at fixed points adjacent their ends, each unit comprising a, pair of elements slidable relative to each other for adjusting the effective iigure forming length of each unit, the paired elements having evenly spaced opposed perfcrations formed therein, a star wheel between the elements having points in geared association with the perforations to maintain the wheel at the mid point of the unit, a plurality of members extending from the star wheel at the mid points of each of the units and connected to the star wheel at the mid points 5 and to pivot points of the other side units of the triangle formed bythe units, the points of connection of said members to the star wheel being maintained at the mid points of the units during adjustment of the I length of the units, said members being extensible to conform to different adjustments of the units.

JOI-1N F. SCHACHT.

REFERENCES CITED Number 10 Number UNITED STATES PATENTS Name Date Hanstein Apr. 3, 1900 Prenveille May 10, 1927 Guyer June 16, 1931 Wellington July 3, 1934 Wolfe Sept. 24, 1946 FOREIGN PATENTS Country Date Great Britain Apr. 18, 1907 

